Simplicial maps for progressive transmission of polygonal surfaces

Abstract

We present a new method for (1) automatically generating multiple Levels Of Detail (LODs) of a polygonal surface, (2) progressively loading, or transmitting, and displaying a surface, and for (3) changing interactively the LOD when displaying. We build the LODs using any algorithm that performs edge collapses and certain vertex removals to simplify surfaces, and provides an ordered list of ordered vertex pairs (edge collapse specifications). We propose a Surface Partition for encoding surface LODs: we define vertex and triangle levels during simplification; vertices and triangles are partitioned and sorted according to their level, and are passed to the display algorithm in decreasing level order, one level at a time, together with a vertex representatives array. Each level of vertices and triangles, together with higher levels and the vertex representatives, form a valid surface. The vertex representatives array encodes a succession of simplicial maps between the highest resolution LOD and other LODs. We propose a data structure using a Directed Acyclic Graph (DAG) for recording a partial ordering among edge collapses, and varying the LODs across the surface. We describe an implementation of our method in VRML. Key-words : Simplicial Map, Edge Collapse, Vertex and Triangle Levels, Surface Levels of Detail, Surface Partition, Progressive Transmission and Display, Dynamic Simplification.